Totally Fuzzy and Relative Poverty Measures

THE MOST COMMON way to measure the prevalence of poverty in a region is to count the number of persons living in households that have incomes below a predetermined income level. This income threshold is known as a poverty line, and the percentage of the population that falls below this poverty line is referred to as the poverty rate or, in technical terms, the headcount index.

One criticism of measuring poverty in this way is the fact that all persons are designated as either “in poverty” or “not in poverty,” with no gradations of any type. For example, a person whose annual income falls a mere $1 below the poverty line would be considered poor while a person with just $2 of additional income would be considered not poor. Some scholars have suggested that rather than thinking of poverty in such black-and-white terms, it would be preferable to think of poverty in a more continuous fashion.

To this end they devised a poverty measure with two different poverty thresholds known as the “totally fuzzy approach” (TFA) to poverty measurement. Under the TFA, all persons with incomes below the lower poverty line would definitely be considered poor while all persons with incomes above the higher poverty threshold would be considered not poor. People between the two lines would count as fractionally poor, depending on how close they were to either threshold.

For example, a person whose income fell exactly halfway between the two thresholds would be considered half poor while a person closer to the upper income line might be considered only one-quarter poor. Under the TFA method, the poverty rate is calculated by adding up all of the fully poor as well as the fractions of the partially poor and dividing by the total population. Five years later, Bruno Cheli and Achille Lemmi expanded on the totally fuzzy approach by altering the way in which the poverty thresholds were calculated. They note that any poverty line is to some extent an arbitrary definition of poverty. Instead of using predetermined income levels as in the totally fuzzy approach, Cheli and Lemmi introduced the Totally Fuzzy and Relative (TFR) poverty measure, under which a person is considered poor or partially poor depending on how her income compares to the national distribution of income. In this way, the need to determine the income levels that define poverty is eliminated. The relative income level at which point a person starts to be considered poor, however, is still a subjective decision.

TFR measures can be modified to be multidimensional so that they combine standard-of-living indicators into a single statistic instead of simply using income as the sole measure of well being. One final advantage of the TFR measurement is that it can be used in the analysis of discrete data and not just continuous data. Discrete data are commonly found in surveys where respondents have a limited number of options from which to choose.